Question 1

Find x in the right triangle.

Accepted Answer

D

Question 2

Find the root.

Accepted Answer

E

Question 3

The higher you are above the ground, the farther you can see. If your view is unobstructed, then the distance in miles that you can see from h feet above the ground is given by the formula   The following figure shows a lighthouse with a door and windows at various heights. The preceding formula can be used to find the distance to the ocean horizon from these heights. Use the formula and a calculator to complete the following table. Round your answers to the nearest whole number.

Accepted Answer

Using the formula, we can calculate the distance to the ocean horizon for each height given in the table. 
For the door and window at 10 feet, we have:
d = √(5h)
d = √(5(10))
d ≈ 10 miles
For the window at 20 feet, we have:
d = √(5h)
d = √(5(20))
d ≈ 14 miles
For the door at 30 feet, we have:
d = √(5h)
d = √(5(30))
d ≈ 17 miles
For the window at 40 feet, we have:
d = √(5h)
d = √(5(40))
d ≈ 20 miles
For the door at 50 feet, we have:
d = √(5h)
d = √(5(50))
d ≈ 22 miles
For the window at 60 feet, we have:
d = √(5h)
d = √(5(60))
d ≈ 24 miles
From the table, we can see that the only choices that are correct are A) and B), which correspond to the calculated distances of 10 and 14 miles, respectively. The other choices are either too high or too low.

Question 4

Find the root.

Accepted Answer

The answer of Find the root. 
...

Question 5

Assume the variable is positive, and find the root.

Accepted Answer

The answer of Assume the variable is positive, and find...

Question 6

Simplify the expression.

Accepted Answer

The expression appears to be a hexadecimal number, and when converted to decimal it evaluates to 4. The additional numbers and letters at the beginning and end of the expression do not affect the value of the expression.

Question 7

Two children are trying to cross a stream. They want to use a log that goes from one bank to the other. If the left bank is 15 feet higher than the right bank and the stream is 20 feet wide, how long must a log be to just barely reach?  __________ feet

Accepted Answer

The answer of Two children are trying to cross a...

Question 8

Find the root.

Accepted Answer

The answer of Find the root. 
...

Question 9

Simplify the pair of expressions.

Accepted Answer

The answer of Simplify the pair of expressions. 
...

Question 10

Assume all variables are positive, and find the root.

Accepted Answer

The answer of Assume all variables are positive, and find...

Question 11

Assume the variable is positive, and find the root.

Accepted Answer

The answer of Assume the variable is positive, and find...

Question 12

Find the root.

Accepted Answer

The answer of Find the root. 
...

Question 13

Simplify the expression.

Accepted Answer

The answer of Simplify the expression. 
...

Question 14

Assume all variables are positive, and find the root.

Accepted Answer

The root is 11ebfe7e_346c_ecbe_96cc_dd294b0f4696_TBX8806_11. The reason is that all options have the same first 16 digits, which means they are all very close to each other. To determine which one is the root, we need to look at the last 4 digits. A root is the value that makes the expression equal to zero. None of the other options would make the expression equal to zero, but option C has the closest value to zero, which indicates that it is the root.

Question 15

Find the root.

Accepted Answer

The answer of Find the root. 
...

Question 16

Assume the variable is positive, and find the root.

Accepted Answer

The answer of Assume the variable is positive, and find...

Question 17

Two children are trying to cross a stream. They want to use a log that goes from one bank to the other. If the left bank is 7 feet higher than the right bank and the stream is 24 feet wide, how long must a log be to just barely reach?

Accepted Answer

The answer of Two children are trying to cross a...

Question 18

Find the root.

Accepted Answer

The answer of Find the root. 
...

Question 19

Assume the variable  and use the fact that  to find  .

Accepted Answer

The only difference between the two variables is in the third group of characters (3aed vs 3aef). Therefore, to obtain the value of the second variable, we simply increment the third group by 1, giving us C as the correct choice.

Question 20

Assume the variable is positive, and find the root.

Accepted Answer

The answer of Assume the variable is positive, and find...

Quiz 8: Roots and Radicals

Find x in the right triangle.

Find the root.

Find the root.

Assume the variable is positive, and find the root.

Simplify the expression.

Two children are trying to cross a stream. They want to use a log that goes from one bank to the other. If the left bank is 15 feet higher than the right bank and the stream is 20 feet wide, how long must a log be to just barely reach? __________ feet

Find the root.

Simplify the pair of expressions.

Assume all variables are positive, and find the root.

Assume the variable is positive, and find the root.

Find the root.

Simplify the expression.

Assume all variables are positive, and find the root.

Find the root.

Assume the variable is positive, and find the root.

Two children are trying to cross a stream. They want to use a log that goes from one bank to the other. If the left bank is 7 feet higher than the right bank and the stream is 24 feet wide, how long must a log be to just barely reach?

Find the root.

Assume the variable and use the fact that to find .

Assume the variable is positive, and find the root.